Former Minnesota Gov. Jesse Ventura leaves the federal courthouse in downtown St. Paul after the first day of his defamation trial against Chris Kyle, the author of the best-selling book "American Sniper," on Tuesday, July 8, 2014. (Pioneer Press: Scott Takushi)

Chris Kyle wanted to keep Jesse Ventura's name out of his autobiography. His wife and his co-author, he said, wanted it in.

It wasn't until Kyle dropped a note in one revision -- "was warned of lawsuit" -- that they agreed to strip the former Minnesota governor's identity from a description of a California bar fight.

The warning had come from a police officer friend, Kyle testified in a deposition. The friend said he should be careful of writing anything unless it was completely true and that he'd probably get sued if it wasn't.

Kyle said he wasn't worried about that. He wasn't "really concerned" about it even after Ventura was outed as the subject of the story and filed a defamation lawsuit against him.

Chris Kyle, author of American Sniper (AP file photo)

Why not? Ventura's attorneys asked.

"Can't defeat the truth," Kyle said.

The remarks came in a November 2012 deposition, a few months before Kyle was killed. They were played Wednesday in federal court in St. Paul as part of Ventura's defamation trial in his lawsuit against Kyle's estate.

Ventura claims Kyle, a decorated veteran of the Iraq war and author of the bestseller "American Sniper," fabricated a story that he punched the former governor after Ventura bad-mouthed the United States and fallen soldiers.

Kyle's estate, represented by his widow, Taya Kyle, says witnesses saw the encounter and that the Ventura story had little to do with the book's success.

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The deposition videos -- about four hours long, with two more to go -- were the longest look jurors in the case are likely to get of the man known as the deadliest military sniper in American history.

Kyle and a friend were fatally shot in 2013 at a Texas gun range, allegedly by a troubled Marine whom they were trying to mentor.

In the deposition, Ventura's attorneys quizzed Kyle on the details of the Ventura story, which the book claims took place at a SEAL hangout near San Diego during a wake for a slain comrade.

Kyle said members of his group noticed Ventura, who served as part of the Underwater Demolition Teams that later merged into the SEALs, sitting and talking with friends.

An injured colleague asked to meet Ventura, a former professional wrestler, actor and media personality. Kyle said he approached Ventura to ask.

Ventura seemed uninterested, Kyle said, but the friend wanted to meet him anyway. They shook hands briefly, and the encounter didn't amount to much.

Later, Ventura was loudly voicing opposition to the war in Iraq, Kyle said. Kyle said he didn't want the families of dead soldiers to hear him and asked Ventura to keep it down.

A back-and-forth between Ventura and other men continued, Kyle said. Eventually, they stepped outside. As Kyle was leaving, he told Ventura he didn't like the way he'd acted, he said.

That's when he claims Ventura told him the SEALs "deserved to lose a few" in the war, leading Kyle to punch Ventura.

Kyle said he ran off afterward because he saw police nearby. He admitted that he didn't witness some elements of the story personally: Ventura falling to the ground, tables flying, the former governor sporting a black eye in the following days.

He believed them to be true, he said, because friends relayed them to him after the fact.

"I assumed it to be true from the sources," he said.

Of particular contention in the deposition was whether Ventura took a swing at Kyle before Kyle allegedly leveled him with a punch.

Did Ventura raise his arm or get a full swing in? asked David Olsen, one of Ventura's lawyers.

He didn't, Kyle said -- he just felt the punch was coming.

"I'm going to ask you one last time," Olsen said. "Did Jesse Ventura swing at you or didn't he?"

"You're going to keep getting the same answer," Kyle said.

"And what answer is that?" Olsen asked.

"That I felt I was fixing to get punched," Kyle said.

Kyle said the story of the fight "has been skewed over the years" and taken on "lots of different versions." But he said his account was true as best he knew it.

Olsen asked if he ever tried to verify the details of the story.

"Besides being involved in it?" Kyle said. "No sir."

He appeared largely at ease through his testimony, at times smiling as he recounted the story and how word of it spread.

Earlier Wednesday, Ventura's attorneys quizzed Kyle's widow about earnings from the book and a movie deal, which they say totaled in the millions.

Kyle said she did not closely track the money, which she and her husband planned to give to needy military families.

When Olsen asked why she hadn't yet given more away, Kyle said she was trying to work out the best way to do so given the tax implications. She added that she was overwhelmed with responsibilities after her husband's death.

Did Kyle ever ask her husband if the Ventura story was true?

"My husband doesn't lie," she said. "It's not something I have to ask."

Olsen asked about a story in "Sniper" in which her husband admitted he lied to a superior officer about a hand injury. According to the story, her husband had said it was from a training accident when it in fact happened in a fight.

She said there was a difference between that and lying about something important, such as when he was under oath.

Olsen also questioned her assertion that her husband didn't like to brag or call attention to himself. Didn't the subtitle on the cover of his book -- "The autobiography of the most lethal sniper in U.S. military history," in all capital letters -- do just that, he asked?

The publisher picked that description, Kyle replied.

In his deposition, Chris Kyle said he was reluctant to write the book until it became apparent that others were pursuing the story.

He said he wanted to tell it himself because he knew if someone else did it, "they were going to make me out to be a braggart."